Can Brain in A Vat learn Math?

Recently, I’ve been thinking about the perpetual illusion scenario which happens by mere chance. I will give a longish presentation for those who missed previous posts on this, and then shortish idea of a direction to think in.


The scenario is your usual brain in a vat / Matrix scenario with one twist – our sensory organs are connected to random generators, so whole illusion happens by mere chance. The twist is there in order to remove any possibility for representational or other indirect causal relation to relevant things which would give rise to the concepts that the BiV might become aware of.

It seems unproblematic that the BiV in such situation, let’s call him Neo, hasn’t become aware of any particular thing in the world, nor he has become aware of any natural kind. But, it seems, that there is no reason to deny that Neo has become aware of the notion of thing in general, the notion of color (in general, and even specific colors in particular), size, form; then notion of causality, change in general (and specific kinds of change in particular, e.g. movement); notion of awareness, notion of other subjects (what some call “other minds”), further – notion of social practices, communication, artifacts and so on…

The reasoning behind this my conviction would go something like this – I can’t see any logical impossibility of connecting a person to such random inputs, in such way that the body is affected in same way as it is affected in reality. Further, I don’t see any logical impossibility for this set of inputs to be generated by a random generator. True, the chance of something like that happening might be 1:gajillion on kajillionth power, but still I don’t see reason to think it is impossible. Now, if we imagine that Neo’s body has had by chance the same ‘inputs’ like mine (also given that we have sufficiently similar bodies), I don’t see a reason why we would assume that he is not having any kind of thought.

But now, if we disconnect Neo and return him into the real world, everything seems OK! We can communicate with him, discuss math problems, discuss social issues, he acts normally (given that his muscles somehow were kept in shape while he was in the vat), and so on.

Even he would use the words for natural kinds normally (and even proper names), I buy the point that his words didn’t mean those things while he was in the vat. They couldn’t mean those things, because he wasn’t aware of those things at all. This is true in same way as a fictional character is still fictional even by mere chance its description and story fits some person exactly. It seems to me that our intuition fights against this conclusion, just because that our thinking because of implausibility right away assumes that there must be some connection between those, but the moment we assume that connection, we have reasons to think that the story is about that person. If somebody has read a story about the fictional person, he can’t say that he knows the real person if somebody doesn’t tell him that “by strange coincidence all the facts about fictional person are true about this real person”. I think the same happens to our intuition in case of Neo’s use of proper names and names of natural kinds – it is our awareness of the fact that everything coincides that pushes our intuition to think that there is a relation between the two. But as posited there are no relation, and Neo can only know that the illusionary facts can be applied to real e.g. rabbits, only if he knows what we do – that by mere chance he got the same inputs like mine. Only with that knowledge, he can feel justified to apply his “knowledge” of illusionary rabbits to real rabbits.

But, the situation seems different to me for those abstract notions I mentioned. I don’t see reason to think that Neo didn’t became aware of Pythagorean theorem while in the vat. To make analogy with the fiction – even some theorem is presented in the fictional story with a proof and everything, it is not as if it is a ‘fictional theorem’. And the same it seems to me goes for all those other abstract notions I named, starting from thing, multitude of things, etc… There is no need for him to somehow ‘transfer’ the fictional facts to some new entities. Those notions are the same ones.

But, then, given that you agree with my reasoning here – the issue appears – how is it possible that Neo has become aware of those things, when he wasn’t at any time acquainted , nor causally related in any relevant way to those things?


So, this has been what has been puzzling me.

One approach is to take those notions as innate in some way. Some form of Kantianism I guess – take those notions as pure concepts of understanding, something that is there prior to any experience. In such a picture it is no wonder that Neo will became aware of them even given the weird events in which he participates. It sounds good, but some of us are not Kantians.

The first idea that came to my mind, and I have already mentioned this, is that Neo became aware of possibilities. For example he didn’t become aware of (any) things, but he became aware of possibility for there to be things. He didn’t became aware of multitudes, but of possibilities for there to be multitudes (couples, triples, etc..). Same for other notions that I mentioned…

But then, those possibilities are possibilities so to say “outside” of the subject. All those possibilities involve possibilities of things which are not the subject himself (Neo).

The idea I want to propose now is that maybe Neo became aware of his abilities to become aware of those possibilities. The abilities to become aware of those possibilities are belonging to the subject himself, to Neo, which would solve the last issue.

However, I’m not sure if there is no some logical problem there. But this is best I can do, I think.